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Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228? Multiple Choice 0.0618 0.2390 0.7600 0.8212

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jennerfranco

Answer:

Step-by-step explanation:

Let X be the random variable that represents a score of Susan. We know that X has a normal distribution with average score of 225 and a standard deviation of 13. For n = 16 games, the average score [tex]\bar{X}[/tex] has a normal distribution with mean of 225 and a standard deviation of [tex]13/\sqrt{16}=13/4=3.25[/tex]. Besides, the z-score related to 220 is (220-225)/3.25=-1.5385, and the z-score related to 228 is (228-225)/3.25= 0.9231. Therefore, we are looking the probability [tex]P(220 < \bar{X} < 228) = P(-1.5385 < Z < 0.9231) = P(Z < 0.9231) - P(Z < -1.5385)[/tex] = 0.76

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